A C*-algebra is a particular type of Banach algebra that is intimately connected with the theory of operators on a Hilbert space. If ℋ is a Hilbert space, then ℬ(ℋ) is an example of a C*-algebra. Moreover, if (Math) is any C*-algebra, then it is isomorphic to a subalgebra of ℬ(ℋ) (see Section 5). Some of the general theory developed in this chapter will be used in the next chapter to prove the Spectral Theorem, which reveals the structure of normal operators.
KeywordsHilbert Space Compact Space Banach Algebra Left Ideal Functional Calculus
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